Point-Guided Denoising

• Point-guided denoising is a class of methods that leverages geometric, statistical, and learned properties of 3D point clouds to suppress noise while preserving critical structures.
• Techniques include density-based (using KDE and mean-shift), graph Laplacian regularization, and advanced score-based deep learning to balance noise reduction with feature retention.
• These methods enhance accuracy in mesh reconstruction and segmentation, as validated by metrics like Chamfer Distance and Hausdorff Distance on complex datasets.

Point-guided denoising refers to a class of methods that leverage the intrinsic geometric, statistical, or learned properties of points within a cloud to selectively suppress noise while preserving underlying structure. In 3D computer vision and graphics, point cloud denoising is essential for accurate mesh reconstruction, object analysis, and downstream tasks such as segmentation. The methodologies for point-guided denoising integrate concepts from optimization, clustering, statistical modeling, and machine learning, frequently combining them in multi-stage pipelines for enhanced robustness and efficiency.

1. Statistical Density-Based Approaches

Early approaches to point-guided denoising utilize the estimated probability density of the observed point set to separate signal from noise and outliers. A prominent representative is the density-based pipeline from (Zaman et al., 2016), which comprises:

• Kernel Density Estimation (KDE) with Adaptive Bandwidth: The core is non-parametric density estimation, employing KDE with a bandwidth parameter that governs the scale of smoothing. Recognizing the sensitivity of KDE to this parameter, an automated bandwidth selection is implemented via particle swarm optimization (PSO), optimizing a LOOCV-based objective:

$$L(H) = \frac{1}{n} \sum_{i=1}^n \log \hat{f}_{H,-i}(x_i)$$

where $H$ denotes the diagonal bandwidth matrix.

• Mean-shift Clustering and Outlier Removal: Mean-shift identifies local density modes, clustering points. Cluster-wise, points are evaluated using a distance-based kNN thresholding scheme—points with abnormally large neighborhood displacements are labeled outliers.
• Bilateral Mesh Filtering: Clusters are triangulated, followed by bilateral filtering to achieve surface smoothing while retaining sharp features, using spatial and range parameters to weight local contributions.

This density-guided, multi-stage process robustly discards outliers, suppresses noise, and preserves salient geometry, with validated efficiency and scalability for high-resolution datasets.

2. Geometric Graph-Based and Manifold Regularization Methods

A significant branch of point-guided denoising research formulates the problem as regularization on graphs constructed to capture local geometry or manifold structure:

• Graph Laplacian Regularization (Zeng et al., 2018): Patches are extracted from the point cloud, with similarity measured via a robust local projection-based distance. Patch-to-patch connections yield a graph, and a Laplacian regularizer is constructed:

$$S_L(\alpha_i) = \sum_{(m, n) \in \mathcal{E}} w_{mn} (\alpha_i(p_m) - \alpha_i(p_n))^2$$

Minimizing a total energy comprised of data fidelity and this regularization encourages patches to remain near their noisy measurements while collaboratively promoting low (local) manifold dimension, suppressing high-frequency noise and preserving structure.

• Total Variation and Bipartite Graphs (Dinesh et al., 2018): Here, a k-NN graph is approximated by a bipartite graph (minimizing KL-divergence of edge weight distributions). Surface normal estimation is integrated into the process, and total variation (GTV) regularization is imposed. The denoising is posed as a convex optimization, solved efficiently by ADMM and proximal gradient descent.
• Octree and Laplacian Smoothing (Cheng et al., 2017): An adaptive octree decomposition is first used for coarse spatial clustering and outlier rejection. Later, Laplacian smoothing is applied not on the full set but on a sparser, mean-summarized representative set, balancing efficiency and surface detail preservation.

These models exploit structural redundancy and the underlying manifold assumption to achieve robust, detail-preserving smoothing, often outperforming naïve geometric or spatial filters particularly on non-uniform and complex noise patterns.

3. Deep Learning and Score-Based Methods

Recent advances exploit deep neural networks to learn the underlying distribution of clean point clouds or the mapping from noisy input to denoised output directly:

• Score-Based Denoising: Neural networks are trained to approximate score functions—gradients of the log-density—of the (possibly unknown) clean point distribution. Denoising is then posed as an iterative process, moving each point along the estimated gradient via gradient ascent. This is seen in several forms:
  • Vanilla Gradient Ascent (Zhao et al., 2022): Each point is updated with the estimate from a neural network interpolated gradient field; momentum schemes are introduced to stabilize updates and reduce inference time.
  • Adaptive and Iterative Schedules (Wang et al., 18 Sep 2025): Rather than fixed step sizes and iteration counts, noise variation is estimated locally, and adaptive schedules are computed for each region, balancing aggressive denoising with feature preservation. The network architecture and training sampling strategies are designed for robust feature and gradient fusion.
  • Uniformity-Enhanced Denoising (Xu et al., 2022): Recognizing that independent score-based updates can lead to non-uniform distributions, an extra interaction term (learned by a lightweight UniNet) is introduced, correcting for local clustering or holes and enabling better surface reconstructions.
• Distribution and Flow-Based Models: Instead of per-point updates, generative models (e.g., normalizing flows) learn invertible mappings between clean and noisy point clouds. PD-Flow (Mao et al., 2022) disentangles noise and structure in latent space; P2P-Bridge (Vogel et al., 29 Aug 2024) refines this via diffusion Schrödinger bridges, learning an optimal transport plan for unordered set interpolation, further strengthened by incorporating color or feature descriptors.
• Unsupervised Score Estimation: Noise2Score3D (Wei, 24 Feb 2025, Wei et al., 12 Mar 2025) removes the need for clean supervision by training a neural network to estimate the score from noisy-only data, leveraging Tweedie's formula:

$\mathbb{E}[X|Y] = Y + \sigma^2 \nabla_Y \log p(Y)$

This enables efficient one-step inference, robust generalization to unseen data, and practical noise-level estimation via a total variation metric designed for point clouds.

4. Dynamic and Spatiotemporal Denoising

Dynamic point clouds, representing moving objects or scenes, present unique challenges due to temporal inconsistency and variable sampling. Point-guided methods for this domain include:

• Spatial-Temporal Graph Learning (Hu et al., 2019): Graphs are constructed across both intra-frame (spatial) and inter-frame (temporal) connections, with a learned Mahalanobis distance metric driving topology. Denoising is framed as a joint optimization of point position and graph structure, balancing data fidelity, spatial smoothness (via Laplacian regularization), and temporal consistency.
• Manifold-to-Manifold and Patch Correspondence (Hu et al., 2020, Hu et al., 2022): By defining a manifold-to-manifold distance using Laplace–Beltrami or graph Laplacian operators, one can dynamically link surface patches across frames. Patches are updated by simulating physical rigid-body motion in the local gradient field, ensuring robust temporal correspondence and refined denoising.

These methods have demonstrated superior temporal coherence and detail preservation relative to static frame-wise approaches in experimental benchmarks.

5. Learnable and Adaptive Filtering

Classic denoising filters—such as bilateral filters—have been revisited in the context of deep learning to address their limitations:

• Learnable Bilateral Filter (LBF) (Si et al., 2022): Bilateral filter parameters are learned via a network, adapting to local geometric features (e.g., estimating spatial/directional variances per-point rather than globally). The network extracts multi-scale context and employs a bi-directional projection loss to enforce geometric faithfulness, with an additional regularization term that ensures uniformity. This approach alleviates the need for manual parameter tuning, and outperforms rigid or heuristically parameterized filters across a range of datasets.
• Fine-Granularity Dynamic Graph Convolutional Networks (GD-GCN) (Xu et al., 21 Nov 2024): By replacing integer-hop propagation in GCNs with micro-step temporal graph convolution integrated via a neural PDE paradigm, the model achieves more continuous adaptation of features, allowing stable and detailed denoising. The use of approximated Riemannian metrics in geometric graph construction enables superior discrimination of geometric structures, especially at boundaries and fine features, and Bernstein polynomial-based spectral filtering guarantees boundedness and diverse frequency response.

6. Benchmarking and Taxonomy

A contemporary survey (Wang et al., 23 Aug 2025) organizes denoising methods along dimensions of supervision (supervised, unsupervised), modeling principle (reconstruction, displacement, distribution, filter, classification), and architectural design trends (from PointNet to graph neural networks and transformers). Unified benchmarks, with protocols for training and metrics such as Chamfer Distance (CD), Hausdorff Distance (HD), and Point-to-Mesh (P2M), are used for comparative evaluation.

Emerging themes and challenges include:

• The advantage of generative/diffusion models for flexible structure modeling.
• Increasing emphasis on unsupervised and self-supervised learning for real-world applicability where clean data is unavailable.
• The need for efficiency and light-weight model designs to enable practical deployment.
• The movement toward global (cloud-level) rather than patch-based denoising for enhanced consistency and fidelity.

7. Summary and Outlook

Point-guided denoising has developed from kernel density/statistical methods and classic optimization, through graph-based and manifold-regularized filtering, to learning-based, deep generative, and diffusion models that incorporate both geometry and statistical learning. By leveraging local context, global structure, temporal consistency, and advanced learning paradigms, these methods have achieved state-of-the-art denoising quality, as measured by CD, HD, and P2M metrics, while preserving essential geometric features.

Ongoing research is focused on combining the best aspects of adaptive local guidance, global coherence, self-supervised learning, and robust, scalable architectures for real-world noisy point cloud data. The integration of efficient noise estimation, uniformity control, and task-aware objectives remains a key challenge and defines the frontier for future developments in this domain.